Music + Math: A Common Equation?

One of Noam D. Elkies' earliest memories is climbing onto his mother's piano bench to practice counting the black and white keys and experiment with sounds.

Today, the 22-year-old Elkies' resume is enough to strike anyone but a Nobel laureate dumb with awe. By the time he graduated first in his class from Columbia at age 19, Elkies had triumphed in several national and international mathematics competitions. In 1987, after garnering his Ph.D. in mathematics in two years, he was named a Harvard Junior Fellow and is currently conducting research in number theory.

Meanwhile, Elkies' musicial compositions have been published, performed professionally and awarded several major prizes. His reputation as a gifted modern composer has advanced throughout New England and beyond. A bass-baritone and piano accompanist for Harvard Glee Club, he continues to compose music under the direction of Rosen Professor of Music Leon Kirchner.

Not surprisingly, Elkies is considered a prodigy in both the Mathematics and Music Departments. "Noam is unlike anyone we've ever had," says Jameson N. Marvin, director of the Glee Club. "His gifted musicality, superior musicianship and sight-reading ability are an extraordinary gift. He's like a Bach or a Mozart."

Donna R. D'Fini, administrative assistant in charge of the math graduate studies program, says Elkies has earned a reputation within the department as a Wunderkind--German for "wonder child." She also says that to her knowledge, no recent math graduate student has bested his two-year record for earning a math Ph.D.


At first glance it might seem that there is something incongruous in the pairing of a seemingly dispassionate discipline with one of the arts. The mathematicians who span both activities explain the connections paradoxically. Music has the rigidity of a math problem in many ways, and math requires bursts of inspiration similar to creative composition, they say.

The more one talks to mathemeticians at Harvard, the clearer it becomes: the Math Department is infested with musical talent. Elkies story is exceptional only in degree.

The Math Department hallway abounds with concert flyers and music schedules tacked on doorways and bulletin boards. One office door bears a typewritten paragraph taken from an obscure 1924 article entitled "Mathematics and Music."

The excerpt, which suggests the possibility of a math-music link, quotes the 17th century mathematician Gottfried Leibniz: "Music is a hidden exercise in arithmetic, of a mind unconscious with dealing with numbers."

Yet the Math Department's musical vibrancy is not only suggested on office doors. One math graduate student, when asked if he had musical interests, boasted of his growing prowess at "change-ringing," an experimental technique of ringing church and hand bells according to mathematical permutations.

Another Math Department bystander darted into his office and returned a few seconds later with a large, awkward wooden object which says was a Renaissance-period ancestor of the flute. After demonstrating how to play the instrument, he passed it around among his friends, some of whom acknowledged that they were already familiar with a modern-day woodwind.

"Most of the people in my department play an instrument--many make career choices between math and music," remarks Math Department Chair Arthur M. Jaffe in an interview, as ancient music floated softly from a nearby compact disk player. Jaffe, proficient at piano and clarinet, habitually conducts "business" in his office to the tune of a favorite concerto or madrigal. "Somehow music seems to appeal to mathemeticians more than, say, reading," he notes.

Jaffe's observation was consistently echoed by faculty and students. Like Jaffe, most mathemeticians say they have noticed an unusually high level of musical awareness and talent among their peers.

What is behind this mysterious math-music link?

"I have a feeling it is more or less the same part of my brain which does both [math and music]," reflects Elkies, "they speak to the same place, the same aesthetic."